ON THE CONDUCTION OF HEAT IN CRYSTALS. 227 ||
a peculiar sort of asymmetry, that we should expect to find traces of their existence. We have seen already that if the crystal possess two planes of symmetry, these constants can have no existence. But the crystalline form (taken as an index of the degree of symmetry of the internal structure) may indicate the non-existence of these constants even in cases in which the crystal does not possess a single plane of symmetry. Take for example quartz, which was one of the crystals employed by M. de Senarrnont in his experiments. In this crystal, not only is there no plane of symmetry, but a peculiar kind of asymmetry is indicated by the occurrence of hemihedral faces, as well as by the optical properties of the crystal. Let three adjacent edges of the primitive rhombohedron meeting in one of the solid angles which is formed by three equal plane angles be denoted by 6r, .ff, /, and let the opposite edges be denoted by (?', H', I'. If we suppose the interior structure to correspond to the crystalline form, whatever we can say of the structure with reference to the edges G} H, /, we can say with reference to the edges JET, I, G, or /, G, H. This shews that the thermic ellipsoid must be an ellipsoid of revolution about the axis of the crystal, and that the line to which GO refers must coincide with the axis. But furthermore, whatever we can say of the structure with reference to G, H, /, we can say with reference to G', I', H'', or J', H', G'} or H', (?', /'. This requires that CD = — CD, and therefore co = 0, and therefore Dl = 0, El = 0, Fl = 0.